Social Shaping of Dynamic Multi-Agent Systems over a Finite Horizon

TL;DR

This paper explores how to design utility functions in multi-agent systems to ensure resource prices stay affordable, using convex optimization and dynamic programming techniques over a finite time horizon.

Contribution

It introduces a method for shaping agent preferences to guarantee socially acceptable prices in dynamic multi-agent resource allocation systems.

Findings

Optimal utility functions can be designed to keep prices within acceptable thresholds.

A quadratic multi-agent LQR formulation provides explicit utility sets.

A numerical algorithm calculates preference parameters ensuring social acceptability.

Abstract

This paper studies self-sustained dynamic multiagent systems (MAS) for decentralized resource allocation operating at a competitive equilibrium over a finite horizon. The utility of resource consumption, along with the income from resource exchange, forms each agent's payoff which is aimed to be maximized. Each utility function is parameterized by individual preferences which can be designed by agents independently. By shaping these preferences and proposing a set of utility functions, we can guarantee that the optimal resource price at the competitive equilibrium always remains socially acceptable, i.e., it never violates a given threshold that indicates affordability. First, we show this problem is solvable at the conceptual level under some convexity assumptions. Then, as a benchmark case, we consider quadratic MAS and formulate the associated social shaping problem as a multi-agent LQR problem which enables us to propose explicit utility sets using quadratic programming and dynamic programming. Finally, a numerical algorithm is presented for calculating the range of the preference function parameters which guarantee a socially accepted price. Some illustrative examples are given to examine the effectiveness of the proposed methods.